ON THE CONCENTRATION OF A SOLCTE. — DAVIS. 295 



In the same way ; 



= — \ al^al -^ ial — (nil - al \ '^al = o 

 •So. If ^ (x-) = _- ( Cos _ .»■ + -Cos - x^^j Cos a; 



+ ^tc ) 



and if x = / then <I> (.r) = — a 



X' = then ^ (r") = « 



I 

 X = - then <J> (.'/; ) = o 



which shows that tiie analysis is correct physically. So that at 

 any time, T 



/ _ 7^2 DT - i^TT^DT 



8a , l^ „ TTX 1 e ^"^ 37r 



- X 



- 257r2DT 



1 / ^ OTT 



4- — e ' Cos 



^ -25 I 



X 



) 



which is a Fourier's Series as i.s readily seen. 



If then we have (J)) the diffusion coefficient of the sub- 

 stance and (7) the length of the solution tube, and (a) the 

 initial difference in concentration at the limiting layer from 

 that at final equilibrium, we can calculate what will be the 

 value of (rt) at any future time. 



Three things are necessary that this change in concentra- 

 tion, due to gravity, may be detected in a solution in a reason- 

 able time: 



(1) The change in density with concentration must be 

 Ini-ge at that concentration. 



(2) The diffusion constant must be as large as possible. 



